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Wave-number selection in pattern-forming systems.
1Department of Physics, Brown University, Providence, Rhode Island 02912, USA.
Physical Review. E
|October 3, 2019
Summary
Noise is key for wave-number selection in pattern-forming systems. Our study shows a unique wave number state emerges over time, regardless of noise strength or initial conditions, confirming noise
Area of Science:
- Physics
- Nonlinear Dynamics
- Statistical Mechanics
Background:
- Wave-number selection in pattern-forming systems is a complex problem.
- External noise has been proposed as a potential mechanism for selection.
Purpose of the Study:
- To investigate the role of noise in wave-number selection.
- To explore the long-time behavior of pattern-forming systems under noise.
Main Methods:
- Conducted extensive numerical simulations.
- Utilized a fast spectral method for integration.
- Studied the noisy stabilized Kuramoto-Sivashinsky equation for large system sizes and long times.
Main Results:
- Identified a unique wave number state with the highest probability at very long times.
- Observed that this selected state is independent of noise strength.
- Confirmed the state's independence from initial conditions.
Conclusions:
- Noise acts as a robust mechanism for state selection in pattern-forming systems.
- The findings provide a convincing case for noise-induced wave-number selection.
- This research advances understanding of pattern formation dynamics.
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